CAIRO, Feb 19 (Reuters) - A shadowy Islamist militant group based in the remote Sinai desert is emerging as a major threat to Egypt's stability, and there are no signs that the army-backed government has devised an effective strategy to contain it.

With assassinations, suicide bombings and shootings, Ansar Bayt al-Maqdis has earned a spot on the global jihad map and its bloody campaign spreading across Egypt is cause for alarm in the West, which sees the biggest Arab nation as a strategic partner.

The group has stepped up attacks on policemen and soldiers since army chief Field Marshal Abdel Fattah al-Sisi toppled Islamist president Mohamed Mursi in July. Hundreds have been killed.

Ansar doesn't have the firepower to defeat Egypt's army, the biggest in the Arab world. But it is proving to be media savvy with a new strategy of targeting foreigners, dealing a devastating blow to tourism, vital for the struggling economy.

"Ansar Bayt al-Maqdis has rapidly become one of the most active jihadist groups in the world and there are strong indications that it is an al Qaeda franchise group," said global intelligence firm Stratfor in a report.

Ansar said it dispatched a suicide bomber who killed two South Koreans and an Egyptian near the town of Taba on Sunday.

The attack is likely to keep foreign tourists, already spooked by political upheaval following the army takeover, away from resorts and ancient sites that once brought in hard currency.

In a video released on YouTube in December, Ansar said its mission had evolved from missile attacks on Israel and blowing up gas pipelines to a bloody campaign against Egyptian security forces and intelligence officials after Mursi's fall.

On Monday, Ansar warned tourists to stay away from Egypt or face attack, part of an apparent tactical shift that could hit the government where it hurts most - the economy.

The stakes are high.

LONG BATTLE BETWEEN STATE AND MILITANTS

Egypt, the heart of the Arab world, has a peace treaty with Israel and contains the Suez Canal. Growing instability could impact the rest of a region already destabilized by the conflict in Syria.

Egyptian security forces have experience fighting militants dating back decades. Islamist-leaning soldiers assassinated President Anwar Sadat in 1981, mainly because of his treaty with Israel. Hosni Mubarak took years to end an Islamist militant insurgency in the 1990s, which left tourism in tatters.

This time, the picture is more complex, with Egypt's political turbulence offering militants opportunities.

Ansar has capitalised on a security vacuum which arose after the 2011 popular uprising that toppled Mubarak.

The group entrenched itself in the Sinai Peninsula's mountains and deserts, forging ties with smugglers, as well as bedouins who have long felt neglected by the central government.

Ansar Bayt al-Maqdis, which means supporters of Jerusalem, has also exploited the struggle between Mursi's Muslim Brotherhood and the army-installed government.

Security forces have been busy with a crackdown against the Brotherhood, killing hundreds in the streets, arresting thousands and jailing its leaders.

That distracted the Interior Ministry from the threat brewing in the Sinai, a 61,000 square km (24,000 square mile) area located between Israel, the Gaza Strip and the Suez Canal.

"They had the space and time to develop in the tumultuous post-Arab Spring period," said Kamran Bokhari, vice president for the Middle East at Stratfor and author of "Political Islam in the Age of Democratization."

While the Brotherhood has been driven underground, the government is still focused on the movement, stamping out protests and prosecuting Mursi and other leaders.

The army has told the public that victory over Ansar is imminent. But Ansar's extensive hit list is growing.

Aside from all the security force members Ansar has killed, it has also claimed responsibility for several high profile assassinations of senior security officials and said it was behind a failed suicide bombing attack on the interior minister in Cairo.

Security has been tightened since those operations and an army offensive has been raging for months in the Sinai, but the attacks keep coming.

Although the government publicly asserts the sheer firepower of the army will eradicate the problem, security officials are far more cautious in private.

"It will take time. We can't ever know if someone is going to blow themselves up. It is hard to prevent suicide attacks," said one.

PRESSURE TO ACT

The government, eager to show that a political road map unveiled by Sisi after Mursi's fall will succeed, does not have much time.

Sisi is expected to announce his candidacy for president soon. Elections, which he is expected to win in a landslide, are due in a few months.

The government wants the process to go smoothly without more Ansar attacks that could shake confidence in security forces.

Sisi's followers regard him as invincible but even they could become disillusioned if Ansar keeps challenging the army.

Some liberals who supported Mursi's overthrow have started to question the hardline tactics of the military and security forces. Some have been jailed.

"The Taba attack, combined with Ansar Bayt al-Maqdis' warning that tourists must leave the country is intended to frustrate economic recovery and to subsequently precipitate greater public opposition to the military establishment," said Anthony Skinner, Middle East and North Africa Director at risk analyst Maplecroft.

Bombs are not the only thing that make Ansar dangerous. Mystery surrounding the group, believed to have about 1,000 fighters, makes it hard to penetrate.

Security officials who monitor the Sinai speak in general terms about the group, saying it evolved from Islamists who established havens in the region after Mubarak's fall.

Weapons smuggled in from chaotic post-Gaddafi Libya, and Sudan, fell into the hands of Ansar fighters, who also convert landmines left in the desert since Egypt's past wars with Israel into roadside bombs, the security officials said.

The government makes no distinction between Ansar and the Brotherhood. But one security official said interrogations of captured Ansar members have not revealed any links.

One thing is clear; easy solutions remain elusive.

"There is no specific time set for ending military operations against the group. A number of its members are in rugged mountain areas. Most move around from one hiding place to another in small pickup trucks " said a military source.

"Many of these people are not known to security forces. We try to find out with interrogations."

Bokhari warned that groups like Ansar are likely to recruit Muslim Brotherhood members so infuriated by the security crackdown that they turn to violence.

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